Why doesn't she text me first?

So I met this girl a few weeks back, I started talking to her first and eventually got her number. We've been talking for a bit now and one night I just decided to put my heart on my sleeve and tell her how I feel about her, however it was in a text message and she didn't get it till the morning. Then a little bit back I asked her how she felt about me and she said she doesn't really know me that well yet so I asked her if she Honestly was still interested in getting to know me and she said That she really was. This girl NEVER texts me or talks to me first, I don't understand it, if she's so interested in getting to know me how come she will never start talking to me first? should I give up?
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Am I just over-analyzing this, does she not text me first just because she expects me to text her? do girls just not text first?
Why doesn't she text me first?
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